(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     11749,        382]
NotebookOptionsPosition[      8533,        290]
NotebookOutlinePosition[     11034,        356]
CellTagsIndexPosition[     10926,        350]
WindowTitle->PaVe
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "See Also",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"See Also", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"PaVeReduce\"\>":>Documentation`HelpLookup[
       "paclet:FeynCalc/ref/PaVeReduce"]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"SeeAlso"]],
      LineSpacing->{1.4, 0}],
     "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\
\[ThickSpace]",
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "URL",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"URL", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"FeynCalc/ref/PaVe\"\>":>
       None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell["FeynCalc/ref/PaVe"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; Null], 
       Delimiter, "\<\"Copy web URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell[
              BoxData[
               MakeBoxes[
                Hyperlink[
                "http://reference.wolfram.com/language/FeynCalc/ref/PaVe.\
html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> 
            False]]; SelectionMove[
         DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; 
        Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
         NotebookLocate[{
           URL[
            StringJoin[
             If[
              TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$207340], 
              "http://reference.wolfram.com/system-modeler/", 
              "http://reference.wolfram.com/language/"], "FeynCalc/ref/PaVe", 
             ".html"]], None}]}]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"URLMenu"]],
      LineSpacing->{1.4, 0}]
    }], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["PaVe", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"PaVe", "[", 
       RowBox[{"i", ",", "j", ",", "...", ",", 
        RowBox[{"{", 
         RowBox[{"p10", ",", "p12", ",", "..."}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"m1", "^", "2"}], ",", 
          RowBox[{"mw", "^", "2"}], ",", "..."}], "}"}]}], "]"}]], 
      "InlineFormula"],
     " \[LineSeparator]denotes the invariant (and scalar) Passarino-Veltman \
integrals, i.e. the coefficient functions of the tensor integral \
decomposition. Joining plist and mlist gives the same conventions as for A0, \
B0, C0, D0. Automatic simlifications are performed for the coefficient \
functions of two-point integrals and for the scalar integrals."
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->156016921],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->231085697],

Cell[TextData[{
 "Some of the PaVe's reduce to special cases with ",
 Cell[BoxData[
  RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}]], "InlineFormula"]
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"PaVe", "[", 
  RowBox[{"0", ",", "0", ",", 
   RowBox[{"{", "pp", "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"m", "^", "2"}], ",", 
     RowBox[{"M", "^", "2"}]}], "}"}], ",", 
   RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellTags->"PaVe",
 CellLabel->"In[1]:=",
 CellID->378525516],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["m", "2"], "-", 
       RowBox[{"2", " ", "m", " ", "M"}], "+", 
       SuperscriptBox["M", "2"], "-", "pp"}], ")"}], " ", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["m", "2"], "+", 
       RowBox[{"2", " ", "m", " ", "M"}], "+", 
       SuperscriptBox["M", "2"], "-", "pp"}], ")"}], " ", 
     FormBox[
      TagBox[
       FormBox[
        RowBox[{
         SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", 
         RowBox[{"pp", ",", 
          SuperscriptBox["m", "2"], ",", 
          SuperscriptBox["M", "2"]}], ")"}],
        TraditionalForm],
       HoldForm],
      TraditionalForm]}], 
    RowBox[{"4", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "D"}], ")"}], " ", "pp"}]], "-", 
   FractionBox[
    RowBox[{
     FormBox[
      TagBox[
       FormBox[
        RowBox[{
         SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", 
         SuperscriptBox["m", "2"], ")"}],
        TraditionalForm],
       HoldForm],
      TraditionalForm], " ", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["m", "2"], "-", 
       SuperscriptBox["M", "2"], "+", "pp"}], ")"}]}], 
    RowBox[{"4", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "D"}], ")"}], " ", "pp"}]], "+", 
   FractionBox[
    RowBox[{
     FormBox[
      TagBox[
       FormBox[
        RowBox[{
         SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", 
         SuperscriptBox["M", "2"], ")"}],
        TraditionalForm],
       HoldForm],
      TraditionalForm], " ", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["m", "2"], "-", 
       SuperscriptBox["M", "2"], "-", "pp"}], ")"}]}], 
    RowBox[{"4", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "D"}], ")"}], " ", "pp"}]]}], 
  TraditionalForm]], "Output",
 ImageSize->{481, 96},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"PaVe",
 CellLabel->"Out[1]="]
}, Open  ]]
}, Open  ]],

Cell["", "SectionFooterSpacer"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "See Also"
}], "SeeAlsoSection",
 WholeCellGroupOpener->True,
 CellID->1255426704],

Cell[TextData[{
 StyleBox[ButtonBox["PaVeReduce",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/PaVeReduce",
  ButtonNote->"PaVeReduce"],
  FontFamily->"Verdana"],
 "."
}], "SeeAlso"]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"PaVe",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 9, 27.675262}", 
    "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "PaVe[i, j, ..., {p10, p12, ...}, {m1^2, mw^2, ...}] denotes the \
invariant (and scalar) Passarino-Veltman integrals, i.e. the coefficient \
functions of the tensor integral decomposition. Joining plist and mlist gives \
the same conventions as for A0, B0, C0, D0. Automatic simlifications are \
performed for the coefficient functions of two-point integrals and for the \
scalar integrals.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "PaVe", 
    "titlemodifier" -> "", "windowtitle" -> "PaVe", "type" -> "Symbol", "uri" -> 
    "FeynCalc/ref/PaVe"}, "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "PrimaryExamplesSection"->{
  Cell[4821, 137, 387, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->156016921]},
 "PaVe"->{
  Cell[5619, 172, 344, 11, 27, "Input",
   CellTags->"PaVe",
   CellID->378525516],
  Cell[5966, 185, 1964, 70, 117, "Output",
   CellTags->"PaVe"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"PrimaryExamplesSection", 10622, 337},
 {"PaVe", 10753, 341}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[576, 21, 2990, 74, 53, "AnchorBarGrid",
 CellID->1],
Cell[3569, 97, 281, 11, 45, "ObjectNameGrid"],
Cell[3853, 110, 943, 23, 119, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[4821, 137, 387, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->156016921],
Cell[CellGroupData[{
Cell[5233, 156, 195, 6, 26, "ExampleSection",
 CellID->231085697],
Cell[5431, 164, 163, 4, 32, "Notes"],
Cell[CellGroupData[{
Cell[5619, 172, 344, 11, 27, "Input",
 CellTags->"PaVe",
 CellID->378525516],
Cell[5966, 185, 1964, 70, 117, "Output",
 CellTags->"PaVe"]
}, Open  ]]
}, Open  ]],
Cell[7957, 259, 31, 0, 29, "SectionFooterSpacer"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8025, 264, 270, 12, 31, "SeeAlsoSection",
 CellID->1255426704],
Cell[8298, 278, 193, 7, 56, "SeeAlso"]
}, Open  ]],
Cell[8506, 288, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

